We present an overview of a wave front sensor-less adaptive optics scheme based upon the optimisation of the low spatial frequency content of images. Aberrations are expanded as a series of Lukosz functions as this permits the independent optimisation of each aberration mode. The scheme is demonstrated in an incoherent transmission microscope. It is shown how the method is related to so-called 'image sharpening' techniques.

Phase Diversity (PD) is a wavefront-sensing technology that offers certain advantages in an Adaptive-Optics
(AO) system. Historically, PD has not been considered for use in AO applications because computations have
been prohibitive. However, algorithmic and computational-hardware advances have recently allowed use of PD
in AO applications. PD is an attractive candidate for AO applications for a variety of reasons. The optical
hardware required is simple to implement and eliminates non-common path errors. In addition, PD has also
been shown to work well with extended scenes that are encountered, for example, when imaging low-contrast solar
granulation. PD can estimate high-order continuous aberrations as well as wavefront discontinuities characteristic
of segmented-aperture or sparse-aperture telescope designs. Furthermore, the fundamental information content
in a PD data set is shown to be greater than that of the correlation Shack-Hartmann wavefront sensor for the
limiting case of unresolved objects. These advantages coupled with recent laboratory results (extended-scene
closed-loop AO with PD sampling at 100 Hz) highlight the maturation of not only the PD concept and algorithm
but the technology as an emerging and viable wavefront sensor for use in AO applications.

This article reports on the novel patent pending Optical Spatial Heterodyne Interferometric Fourier Transform Technique
(the OSHIFT technique), the resulting interferometer also referred to as OSHIFT, and its preliminary results. OSHIFT
was borne out of the following requirements: wavefront sensitivity on the order of 1/100 waves, high-frequency
wavefront spatial sampling, snapshot 100Hz operation, and the ability to deal with discontinuous wavefronts. The first
two capabilities lend themselves to the use of traditional interferometric techniques; however, the last two prove difficult
for standard techniques, e.g., phase shifting interferometry tends to take a time sequence of images and most
interferometers require estimation of a center fringe across wavefront discontinuities. OSHIFT overcomes these
challenges by employing a spatial heterodyning concept in the Fourier (image) plane of the optic-under-test. This
concept, the mathematical theory, an autocorrelation view of operation, and the design with results of OSHIFT will be
discussed. Also discussed will be future concepts such as a sensor that could interrogate an entire imaging system as
well as a methodology to create innovative imaging systems that encode wavefront information onto the image. Certain
techniques and systems described in this paper are the subject of a patent application currently pending in the United
States Patent Office.

A proof-of-concept phase diversity (PD) wavefront sensing and control (WFS&C) testbed has been developed that
displays 5/1,000 wave RMS accuracy, operates at a sample rate of 100Hz, uses the extended scene of interest in lieu of a
guide star, and is comprised of all low-cost commercial-off-the-shelf (COTS) parts - including the PD processor. This testbed allows closed-loop
operation via a dual deformable-mirror (DM) concept where two DMs are optically conjugate to the exit pupil: one
acting as an independent disturbance and the other reacting to PD WFS&C commands in order to correct the system
wavefront. The use of low-cost, COTS components demonstrated the flexibility of a PD-only
WFS&C approach, and additionally allowed for this system to be conceived, designed, assembled and brought to
operation in approximately nine months. Automatic calibration efforts begun on this testbed have allowed for the quick
discrimination of prominent PD forward-model parameters and a more rapid verification and validation (V&V) process.
Also aiding the V&V process is a novel spatial-heterodyning optical interferometer that collects all information in a
single snapshot and may be made synchronous with the fast PD sample rate. This demonstration proves a PD-only
WFS&C subsystem capability suitable for use on a wide variety of adaptive-optics imaging systems.

This paper will report on efforts to automatically calibrate in situ a phase-diversity (PD) wavefront sensing and control
(WFS&C) system, the results of which are demonstrated on the General Dynamics Advanced Information System's
(GDAIS') QuickStar testbed1, a dual deformable mirror (DM) system which operates at 100Hz sampling rate. The
iterative automatic calibration (AutoCal) process includes both coarse and fine calibration modes, initial closed-loop
flattening of the commercial-off-the-shelf (COTS) DMs, estimation of the system's static wavefront - including DM
print-through, determination of PD-derived actuator influence functions, formulating the resulting system matrix and the
resulting forward-model parameters. Analyses of the system after the calibration routines shows low-order WFS
accuracy of ~0.005λ RMS and closed-loop residual wavefront measurement of ~0.002λ. All of these results were
accomplished with a software package that takes on the order of one hour to operate.

The outcomes of research at the Durham University Centre for Advanced Instrumentation into
the use of low cost devices in the construction and operation of adaptive optics systems is
presented. An embedded low cost sensing and control system for high speed AO is presented
where the components for sensing and control cost under us$400 and we demonstrate the
possibility to build and operate an AO system where the sensor and controller have a combined
cost of under us$150. An alternative application of the work as a data processing smart camera
is presented.

Electro-static membrane mirrors have been in use for over ten years in active and adaptive optics
applications in industrial, academic, and research systems. We introduce a deformable membrane mirror
produced from commercial off the shelf (COTS) pellicle membranes. This greatly reduces production costs
of the device. The device can be produced in up to 3 inch formats without large static aberrations. The
mirror is capable of closed loop bandwidth in excess of several hundred Hz. Measurements of the device
influence functions will be presented along with results of closed loop real time control performance
measurements.

This document proposes a method to achieve full-sky adaptive optic coverage using a laser guidestar (LGS)
adaptive optics (AO) system. This is done by stabilizing the sodium beacon by using information from the
uplink beam so that the downlink tilt, i.e. the atmospheric tilt, can be measured.
It is commonly known that tilt cannot be measured from a laser guidestar beacon because the uplink and
downlink beams experience the same atmospheric tilt. This is true in itself, but disregards information that
can be obtained from the uplink beam. Because the atmospheric structure function is a maximum near the exit
aperture and decreases exponentially with altitude, the uplink beam accumulates most of its tilt near the exit
aperture. For instance, when using the Hufnagel-Valley atmospheric model with A = 1.7 x 10-14 and W = 21,
&gsim; 92% of uplink atmospheric tilt occurs at altitudes below 5Km and 97% by ∼ 20Km. So, the instantaneous
position of the uplink beam along the uplink path can be a predictor of the instantaneous position of the sodium
beacon; this is this paper's main result. Further, a means of measuring tilt from the uplink beam from its
Rayleigh backscatter is presented and for some of the parameters and geometries considered, it is shown that
the uplink tilt can be measured at sufficiently high altitudes and camera frames rates that a control system can
stabilize the uplink beam, which in-turn stabilizes the sodium beacon, thus allowing atmospheric downlink tilt
to be measured. Assuming that such a control loop can be implemented, such stabilization would allow for full
sky laser guide star operation with AO performance similar to current LGS AO systems using off-axis natural
guide stars.

Lead magnesium niobate (PMN) actuators are electrostrictive actuators with high dynamic range used in deformable
mirrors. Actuator fault detection in deformable mirrors typically occurs through optical testing. We developed a nonoptical
method for detecting actuator faults via low electric field resonance testing. The low electric field resonance
method is standard practice for characterizing piezoelectric materials. The piezoelectric/electrostrictive coefficient
couples the electrical and mechanical impedance of the actuator; a change in the mechanical boundaries (force) on the
actuator results in a shift of the impedance resonances. We demonstrate experimentally that a PMN actuator can fracture
but retain functionality under compression and that the fracture can be detected by measuring the impedance resonances
at various bias voltages (various values of tension and compression). A concurrent optical test using a displacement
interferometer was used to corroborate the results. We propose the impedance resonance approach as a non-optical fault
detection test for in-situ actuators.

Wave front precision distortion correction and transformation using a Liquid Crystal Spatial Light Modulator (LC
SLM) is discussed. After passing through non perfect elements, a coherent beam becomes a distortional beam. The
distortion is expressed in either optical paths difference or phase difference way. The difference is measured
quantitatively. SLM modulates the phase of the beam in a pixel resolution. The beam is recovered to a plane wave
front again after the correction. The accuracy of the modulation is 0.0165λ.

Many electro optical devices are now available for compensating atmospheric distortions in optical systems. To support the characterization of these devices in a consistent fashion a common testbed that physically simulates these atmospheric aberrations is required. This paper reports on a system that realizes seeing conditions ranging from very poor to excellent and feeds these wavefronts to the compensation device under test. The testbed provides quantitative characterization of the system under test and evaluates residual wavefront error.

Sandia National Laboratory has constructed several segmented MEMS deformable mirrors that are under investigation for their suitability in experimental Adaptive Optics systems for the Naval Research Laboratory. These mirrors are fabricated in a hexagonal array and can been constructed with flat surfaces, or with optical power allowing each mirror to bring its subaperture of light to a focus similar to a Shack-Hartman array. Each mirror can use the tip, tilt and piston function to move the focused spots to the desired reference location, and the measurement of the applied voltage can be used directly to power a similar flat MEMS deformable mirror. Unlike the Shack-Hartman array, this wavefront sensor can detect large magnitude aberrations up to and beyond where the focused spots overlap, due to the ability to dither each focused spot. This paper reports on experiments and analysis of the open-loop performance, including repeatability measurements.

For a non-cooperative target, a laser beacon is created by illuminating the target with a beacon beam. When a beacon
beam propagates though deep turbulence, turbulence spreads the beam. A conventional phase conjugate adaptive optics
(AO) system is not efficient in the presence of Beacon Anisoplanatism when the beacon beam spot size at the target
includes many isoplanatic patch sizes. We introduce a concept of the wavefront-based stochastic parallel gradient decent
(WSPGD) AO system, which uses an off-axis wavefront sensor to provide feedback for the beam control algorithm. This
concept is based on the finding that the phase aberrations of laser return from the target contain information about beam
spot size at the target, and that correction of a limited number of low-order Zernike modes increases on-axis intensity
and power in the bucket at the target. We evaluated the WSPGD AO system performance in simulation for two tactical
engagement scenarios in the presence of strong turbulence. We found that that the WSPGD AO system can efficiently
compensate the effects of strong turbulence including Beacon Anisoplanatism, even when the beam spot size at the
target includes up to 20 isoplanatic patch sizes and the isoplanatic angle is by a factor of 2.6 less than the diffraction
limit. The Strehl ratio gain for this scenario is 1.6 - 2.5, and the maximum Strehl ratio is achieved after 15-20 iterations.
A laboratory demonstration performed under a separate program confirmed our theoretical predictions.

A concept of a Hybrid Wavefront-based Stochastic Parallel Gradient Decent (WSPGD) Adaptive Optics
(AO) system for correcting the combined effects of Beacon Anisoplanatism and Thermal Blooming is
introduced. This system integrates a conventional phase conjugate (PC) AO system with a WSPGD AO
system. It uses on-axis wavefront measurements of a laser return from an extended beacon to generate
initial deformable mirror (DM) commands. Since high frequency phase components are removed from the
wavefront of a laser return by a low-pass filter effect of an extended beacon, the system also uses off-axis
wavefront measurements to provide feedback for a multi-dithering beam control algorithm in order to
generate additional DM commands that account for those missing high frequency phase components.
Performance of the Hybrid WSPGD AO system was evaluated in simulation using a wave optics code.
Numerical analysis was performed for two tactical scenarios that included ranges of L = 2 km and L = 20
km, ratio of aperture diameter to Fried parameter, D/r0, of up to 15, ratio of beam spot size at the target to
isoplanatic angle, θB/θ0, of up to 40, and general distortion number characterizing the strength of Thermal
Blooming, Nd = 50, 75, and 100. A line-of-sight in the corrected beam was stabilized using a target-plane
tracker. The simulation results reveal that the Hybrid WSPGD AO system can efficiently correct the effects
of Beacon Anisoplanatism and Thermal Blooming, providing improved compensation of Thermal
Blooming in the presence of strong turbulence. Simulation results also indicate that the Hybrid WSPGD
AO system outperforms a conventional PC AO system, increasing the Strehl ratio by up to 300% in less
than 50 iterations. A follow-on laboratory demonstration performed under a separate program confirmed
our theoretical predictions.

This paper uses a Kalman filter to estimate the optical wavefront
from the interferograms produced by a temporally phase-shifted
self referencing interferometer (SRI). Four methods of estimation
are evaluated with varying noise strengths and frame rates. An
extended Kalman filter is shown to outperform other estimation
methods and expand the conditions under which a temporal SRI can
be utilized.

When it comes to controlling the laser beam parameters (i.e. angular divergence and shape) detection and
characterization of its wavefront is essential for enhancing beam delivery and operational efficiency of laser based
systems in commercial, industrial, medical or military applications. This is even more important when the laser beam
propagates in real atmosphere where turbulence effects strongly degrades its quality and substantially reduces
energy/power density delivered to the target. This presentation discusses a wavefront sensor, with its performance based
upon the principle of the phase shifting interferometry (PSI). The latter enables instantaneous characterization of a
wavefront. The interferometric essence of the PSI operation makes it possible to measurement the complex amplitude of
the optical field, thus allowing retrieval of the complete information of the detected wave.

Diffractive beam direction needs to be controlled agilely and precisely in beam steering and some diffraction
applications. Far field fringe generation, wave front distortion correction by employing programmable diffractive element
is a new interesting research area. A phase-only liquid crystal spatial light modulator is used to produce arbitrary
fringes expected.
For the practical application, the main technology we tried includes: 1) the fast recovering speed from arbitrary fringe
to the phase distribution of liquid crystal spatial light modulator, 2) the expected fringe light intensity information is
delivered by phase information. The previous G-S phase recovering algorithm demands more iterative calculations,
which is not suitable for real time purpose. According to the statistics of light field distribution of expected fringes, a
pseudorandom phase encoding method has been used in this work. The expected fringe light intensity information is used
to limit the initial value for phase recovering calculation. By this way, the iterative time has been reduced largely, and
the phase recovering is optimized as well. The expected diffraction fringe can be obtained through 3-5 iterative
calculations.
The experiment results show that the technology is satisfactory for fast applications.

The application of adaptive optics has been hindered by the cost, size, and complexity of the systems. We describe here
progress we have made toward creating low-cost compact turn-key adaptive optics systems. We describe our new low-cost
deformable mirror technology developed using polymer membranes, the associated USB interface drive
electronics, and different ways that this technology can be configured into a low-cost compact adaptive optics system.
We also present results of a parametric study of the stochastic parallel gradient descent (SPGD) control algorithm.

Multi-Conjugate Adaptive-Optical (MCAO) systems have been proposed as a means of compensating both
intensity and phase aberrations in a beam propagating through strong-scintillation environments. Progress made
on implementing a MCAO system at the Starfire Optical Range (SOR), Air Force Research Laboratory, Kirtland
AFB, is discussed. In previous work, it was shown that the First-stage Intensity Redistribution Experiment
(FIRE) controlled and compensated wavefront intensity for static cases. As a secondary step toward controlling
a two deformable mirror (DM) system, the FIRE experimental layout is used to examine another aspect of an
MCAO system faster control of wavefront intensity. The FIRE experimental layout employs two wavefront
sensors (WFS) and a single DM. One WFS is placed conjugate to the DM while the second WFS is located at a
distance which produces a desired Fresnel number for the propagation between theWFSs. A modified Gerchberg-
Saxton (GS) algorithm that propagates between image planes is employed for determining DM commands. The
forward and back propagation portion of each GS iteration are computed in software. Using the GS solution, a
control loop is closed on a WFS reconstructor in order to maintain beam shape in moving optical turbulence.
The forward propagation phase pattern produced by the GS algorithm is tailored, via constraints, so that beam
propagation along the path between the two WFSs produces a desired intensity profile and minimizes phase
aberrations at the second WFS. In the next phase of MCAO development, a second DM will be added conjugate
to the second WFS in order to correct the remaining phase aberrations.

Phase-only liquid-crystal spatial light modulators (SLMs) provide an excellent means of producing electrically
controllable, dynamic, and repeatable aberrations. Emulating the aberrating effects of atmospheric turbulence
is the application studied here. This paper implements a new method for designing a SLM-based turbulent path
in the laboratory. The turbulent path was constructed with well-calibrated SLMs and was subsequently used
to implement an appropriately scaled ground-to-air laser engagement. After propagation through the turbulent
path, the irradiance and phase properties of the aberrated light were measured with an image sensor and a Shack-Hartmann wavefront sensor, respectively. The resulting wave structure functions and log-amplitude probability
densities showed excellent agreement with theoretical expectations and the results of wave-optics simulations.

Imaging through turbulence using adaptive optics (AO) is limited by scintillation, even with perfect wavefront sensing
and reconstruction. Such errors can be mitigated in closed loop by multi-conjugate AO systems consisting of two phase
correctors, each of which is driven by a pair of wavefront sensor phase measurements, along with an internal probe
beam that samples the beam train along a common path while propagating in the opposite direction as the external
signal beam or beacon wavefront that samples the turbulence. Such decentralized architectures avoid not only direct
measurement and feedback of irradiance but also intensive and/or highly coupled nonlinear control algorithms in favor
of simpler, more conventional linear control laws. They also admit linear dynamical-systems modeling in the spatial-frequency
domain. In this framework, coupled scintillation and servo-lag wave correction errors induced by turbulence
are here predicted parametrically by scalably filtering and numerically integrating power spectral density profiles. The
role of regularization is explored, and comparisons to previous nonlinear wave-optic simulation results are made.

Quantifying the results for a multi-conjugate adaptive optics (MCAO) system is more complex than a
traditional adaptive optics (AO) system. The complexity of analyzing a MCAO system stems from using
multiple deformable mirrors (DMs) and quantifying the influence functions at the wavefront sensor (WFS).
In this paper, analysis tools are developed to quantify MCAO performance. Influence functions from two
deformable mirrors are propagated to a WFS using CODEV to simulate an MCAO design comparable to
the Dunn Solar Telescope (DST). Using MATLAB, the propagated influence functions are mapped to the
appropriate field positions, and reconstructor matrices are built using the mapped influence functions. Next,
a correctability analysis was performed using theoretical random phase screens. The developed tools are
versatile and useful as a system design tool and in a laboratory setting.

A MATLAB toolbox has been developed for wavefront control of segmented optical systems. The toolbox
is applied to the optical models of the James Webb Space Telescope (JWST) in general and to the JWST
Testbed Telescope (TBT) in particular, implementing both unconstrained and constrained wavefront
optimization to correct for possible misalignments of the segmented primary mirror or the monolithic
secondary mirror. The optical models are implemented in the ZEMAX optical design program and
information is exchanged between MATLAB and ZEMAX via the Dynamic Data Exchange (DDE)
interface. The model configuration is managed using the Extensible Markup Language (XML) protocol.
The optimization algorithm uses influence functions for each adjustable degree of freedom of the optical
model. Both iterative and non-iterative algorithms have been developed that converge to a local minimum
of the root-mean-square (rms) wavefront error using singular value decomposition (SVD) of the control
matrix of influence functions. The toolkit is highly modular and allows the user to choose control
strategies for the degrees-of-freedom (DOF) on a given iteration and also allows the wavefront
convergence criterion to be checked on each iteration. As the influence functions are nonlinear over the full
control parameter space, the toolkit also allows for trade-offs between frequency of updating the local
influence functions and execution speed. The functionality of the toolbox and the validity of the underlying
algorithms have been verified through extensive simulations.

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